Question
Which situations are independent?
Select all that apply.
Question 1 options:
A coin is flipped three times.
A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.
A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.
A jar contains twenty coins. Two coins are picked randomly with replacement.
Select all that apply.
Question 1 options:
A coin is flipped three times.
A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.
A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.
A jar contains twenty coins. Two coins are picked randomly with replacement.
Answers
GPT-4o mini
To determine which situations are independent, we need to understand that two events are independent if the outcome of one does not affect the outcome of the other.
Hereβs the analysis for each option:
1. **A coin is flipped three times.**
- Each flip is independent of the previous flips. The outcome of one flip does not affect the outcome of the others.
- **Independent.**
2. **A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.**
- The second draw is dependent on the first because the total number of balls changes after the first draw (since itβs without replacement).
- **Not independent.**
3. **A spinner contains 3 equal sectors labeled A, B, and C. The spinner is spun twice.**
- Each spin is independent of the others. The outcome of the first spin does not affect the outcome of the second spin.
- **Independent.**
4. **A jar contains twenty coins. Two coins are picked randomly with replacement.**
- Because the selection is with replacement, the outcome of the first coin does not affect the outcome of the second coin.
- **Independent.**
Based on this analysis, the independent situations are:
- A coin is flipped three times.
- A spinner contains 3 equal sectors labeled A, B, and C. The spinner is spun twice.
- A jar contains twenty coins. Two coins are picked randomly with replacement.
Hereβs the analysis for each option:
1. **A coin is flipped three times.**
- Each flip is independent of the previous flips. The outcome of one flip does not affect the outcome of the others.
- **Independent.**
2. **A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.**
- The second draw is dependent on the first because the total number of balls changes after the first draw (since itβs without replacement).
- **Not independent.**
3. **A spinner contains 3 equal sectors labeled A, B, and C. The spinner is spun twice.**
- Each spin is independent of the others. The outcome of the first spin does not affect the outcome of the second spin.
- **Independent.**
4. **A jar contains twenty coins. Two coins are picked randomly with replacement.**
- Because the selection is with replacement, the outcome of the first coin does not affect the outcome of the second coin.
- **Independent.**
Based on this analysis, the independent situations are:
- A coin is flipped three times.
- A spinner contains 3 equal sectors labeled A, B, and C. The spinner is spun twice.
- A jar contains twenty coins. Two coins are picked randomly with replacement.